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Structure preserving simulation of monopedal jumping
Author(s) -
Koch Michael W.,
Leyendecker Sigrid
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210027
Subject(s) - variational integrator , correctness , computation , jump , symplectic geometry , integrator , multibody system , mathematics , optimal control , computer science , control theory (sociology) , mathematical optimization , control (management) , classical mechanics , algorithm , mathematical analysis , physics , computer network , bandwidth (computing) , quantum mechanics , artificial intelligence
This work considers the structure preserving simulation of three‐dimensional multibody dynamics with contacts. The used variational integrator is based on a discrete version of the Lagrange‐d'Alembert principle, which yields a symplectic momentum method. One of our main goals is to guarantee the structure preservation and the geometric correctness, thus we solve the non‐smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non‐smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a finite dimensional constrained optimisation problem. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)